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3 (three) is a
number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
, numeral and digit. It is the
natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following 2 and preceding 4, and is the smallest odd
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
and the only prime preceding a square number. It has religious and cultural significance in many societies.


Evolution of the Arabic digit

The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and
Chinese numerals Chinese numerals are words and characters used to denote numbers in written Chinese. Today, speakers of Chinese languages use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more fami ...
) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the
Gupta Empire The Gupta Empire was an Indian empire during the classical period of the Indian subcontinent which existed from the mid 3rd century to mid 6th century CE. At its zenith, the dynasty ruled over an empire that spanned much of the northern Indian ...
the sign was modified by the addition of a curve on each line. The
Nāgarī script The Nāgarī script is the ancestor of Devanagari, Nandinagari and other variants, and was first used to write Prakrit and Sanskrit. The term is sometimes used as a synonym for Devanagari script.Kathleen Kuiper (2010), The Culture of India, New ...
rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. The Indian digits spread to the
Caliphate A caliphate ( ) is an institution or public office under the leadership of an Islamic steward with Khalifa, the title of caliph (; , ), a person considered a political–religious successor to the Islamic prophet Muhammad and a leader of ...
in the 9th century. The bottom stroke was dropped around the 10th century in the western parts of the Caliphate, such as the
Maghreb The Maghreb (; ), also known as the Arab Maghreb () and Northwest Africa, is the western part of the Arab world. The region comprises western and central North Africa, including Algeria, Libya, Mauritania, Morocco, and Tunisia. The Maghreb al ...
and
Al-Andalus Al-Andalus () was the Muslim-ruled area of the Iberian Peninsula. The name refers to the different Muslim states that controlled these territories at various times between 711 and 1492. At its greatest geographical extent, it occupied most o ...
, when a distinct variant ("Western Arabic") of the digit symbols developed, including modern Western 3. In contrast, the Eastern Arabs retained and enlarged that stroke, rotating the digit once more to yield the modern ("Eastern")
Arabic Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns lang ...
digit "٣". In most modern Western
typeface A typeface (or font family) is a design of Letter (alphabet), letters, Numerical digit, numbers and other symbols, to be used in printing or for electronic display. Most typefaces include variations in size (e.g., 24 point), weight (e.g., light, ...
s, the digit 3, like the other
decimal digit A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1"), or in combinations (such as "15"), to represent numbers in positional notation, such as the common base 10. The name "digit" originate ...
s, has the height of a
capital letter Letter case is the distinction between the letters that are in larger uppercase or capitals (more formally ''majuscule'') and smaller lowercase (more formally '' minuscule'') in the written representation of certain languages. The writing system ...
, and sits on the baseline. In typefaces with
text figures Text figures (also known as non-lining, lowercase, old style, ranging, hanging, medieval, billing, or antique figures or numerals) are numerals designed with varying heights in a fashion that resembles a typical line of running text, hence the ...
, on the other hand, the glyph usually has the height of a lowercase letter "x" and a descender: "". In some French text-figure typefaces, though, it has an ascender instead of a descender. A common graphic variant of the digit three has a flat top, similar to the letter Ʒ (ezh). This form, sometimes called a banker's 3, can stop a forger from turning the 3 into an 8. It is found on UPC-A barcodes and
standard 52-card deck The standard 52-card deck of French-suited playing cards is the most common pack of playing cards used today. The main feature of most playing card decks that empower their use in diverse games and other activities is their double-sided design, w ...
s.


Mathematics


Divisibility rule

A
natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
is
divisible In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a '' multiple'' of m. An integer n is divisible or evenly divisibl ...
by 3 if the sum of its digits in
base 10 The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of t ...
is also divisible by 3. This known as the
divisibility rule A divisibility rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed Divisor (number theory), divisor without performing the division, usually by examining its digits. Although there are divisibility test ...
of 3. Because of this, the reverse of any number that is divisible by three (or indeed, any
permutation In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first mean ...
of its digits) is also divisible by three. This divisibility rule works in any
positional numeral system Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system ...
whose base divided by three leaves a remainder of one (bases 4, 7, 10, etc.).


Properties

3 is the second smallest
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
and the first odd prime number. 3 is a
twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
with 5, and a cousin prime with 7. A
triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
is made of three sides. It is the smallest non-self-intersecting
polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
and the only polygon not to have proper diagonals. When doing quick estimates, 3 is a rough approximation of , 3.1415..., and a very rough approximation of ''e'', 2.71828... 3 is the first
Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 1 ...
. 3 is also the first of five known
Fermat prime In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form:F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: 3, 5, ...
s. It is the second Fibonacci prime (and the second Lucas prime), the second
Sophie Germain prime In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +&nbs ...
, and the second
factorial prime A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are : : 2 (0! + 1 or 1! + 1) ...
. 3 is the second and only prime
triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
, and
Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...
proved that every integer is the sum of at most 3
triangular numbers A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
. Three is the only prime which is one less than a perfect square. Any other number which is n^2 − 1 for some integer n is not prime, since it is (n − 1)(n + 1). This is true for 3 as well (with n = 2), but in this case the smaller factor is 1. If n is greater than 2, both n − 1 and n + 1 are greater than 1 so their product is not prime.


Numeral systems

There is some evidence to suggest that early man may have used counting systems which consisted of "One, Two, Three" and thereafter "Many" to describe counting limits. Early peoples had a word to describe the quantities of one, two, and three but any quantity beyond was simply denoted as "Many". This is most likely based on the prevalence of this phenomenon among people in such disparate regions as the deep Amazon and Borneo jungles, where western civilization's explorers have historical records of their first encounters with these indigenous people.


List of basic calculations


Engineering

*The
triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
, a
polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
with three edges and three vertices, is the most stable physical shape. For this reason it is widely utilized in construction, engineering and design.


Pseudoscience

*Three is the symbolic representation for Mu, Augustus Le Plongeon's and James Churchward's lost continent.


Religion and beliefs

Many world religions contain triple deities or concepts of trinity, including the
Hindu Hindus (; ; also known as Sanātanīs) are people who religiously adhere to Hinduism, also known by its endonym Sanātana Dharma. Jeffery D. Long (2007), A Vision for Hinduism, IB Tauris, , pp. 35–37 Historically, the term has also be ...
Trimurti The Trimurti ( /t̪ɾimʊɾt̪iː/) is the triple deity of supreme divinity in Hinduism, in which the cosmic functions of creation, preservation, and destruction are personified as a triad of deities. Typically, the designations are that ...
and Tridevi, the
Triglav Triglav (; ; ), with an elevation of , is the highest mountain in Slovenia and the highest peak of the Julian Alps. The mountain is the pre-eminent symbol of the Slovene nation, appearing on the Coat of arms of Slovenia, coat of arms and Flag ...
(), the chief god of the
Slav The Slavs or Slavic people are groups of people who speak Slavic languages. Slavs are geographically distributed throughout the northern parts of Eurasia; they predominantly inhabit Central Europe, Eastern Europe, Southeastern Europe, and N ...
s, the three Jewels of
Buddhism Buddhism, also known as Buddhadharma and Dharmavinaya, is an Indian religion and List of philosophies, philosophical tradition based on Pre-sectarian Buddhism, teachings attributed to the Buddha, a wandering teacher who lived in the 6th or ...
, the three Pure Ones of
Taoism Taoism or Daoism (, ) is a diverse philosophical and religious tradition indigenous to China, emphasizing harmony with the Tao ( zh, p=dào, w=tao4). With a range of meaning in Chinese philosophy, translations of Tao include 'way', 'road', ' ...
, the
Christian A Christian () is a person who follows or adheres to Christianity, a Monotheism, monotheistic Abrahamic religion based on the life and teachings of Jesus in Christianity, Jesus Christ. Christians form the largest religious community in the wo ...
Trinity The Trinity (, from 'threefold') is the Christian doctrine concerning the nature of God, which defines one God existing in three, , consubstantial divine persons: God the Father, God the Son (Jesus Christ) and God the Holy Spirit, thr ...
, the
greek Greek may refer to: Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group *Greek language, a branch of the Indo-European language family **Proto-Greek language, the assumed last common ancestor of all kno ...
goddess hecate and the Triple Goddess of
Wicca Wicca (), also known as "The Craft", is a Modern paganism, modern pagan, syncretic, Earth religion, Earth-centred religion. Considered a new religious movement by Religious studies, scholars of religion, the path evolved from Western esote ...
. According to
Pythagoras Pythagoras of Samos (;  BC) was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of P ...
and the Pythagorean school, the number 3, which they called ''triad'', is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.


As a lucky or unlucky number

Three (, formal writing: ,
pinyin Hanyu Pinyin, or simply pinyin, officially the Chinese Phonetic Alphabet, is the most common romanization system for Standard Chinese. ''Hanyu'' () literally means 'Han Chinese, Han language'—that is, the Chinese language—while ''pinyin' ...
''sān'',
Cantonese Cantonese is the traditional prestige variety of Yue Chinese, a Sinitic language belonging to the Sino-Tibetan language family. It originated in the city of Guangzhou (formerly known as Canton) and its surrounding Pearl River Delta. While th ...
: ''saam''1) is considered a good number in
Chinese culture Chinese culture () is one of the Cradle of civilization#Ancient China, world's earliest cultures, said to originate five thousand years ago. The culture prevails across a large geographical region in East Asia called the Sinosphere as a whole ...
because it sounds like the word "alive" ( pinyin ''shēng'', Cantonese: ''saang''1), compared to four (, pinyin: ''sì'', Cantonese: ''sei''1), which sounds like the word "death" ( pinyin ''sǐ'', Cantonese: ''sei''2). The phrase " Third time's the charm" refers to the superstition that after two failures in any endeavor, a third attempt is more likely to succeed. However, some superstitions say the opposite, stating that
luck Luck is the phenomenon and belief that defines the experience of improbable events, especially improbably positive or negative ones. The Naturalism (philosophy), naturalistic interpretation is that positive and negative events may happen at a ...
, especially bad luck, is often said to "come in threes". One such superstition, called " Three on a Match", says that it is unlucky to be the third person to light a cigarette from the same match or lighter. This superstition is sometimes asserted to have originated among soldiers in the trenches of the First World War when a sniper might see the first light, take aim on the second and fire on the third.


See also

*
Cube (algebra) In arithmetic and algebra, the cube of a number is its third exponentiation, power, that is, the result of multiplying three instances of together. The cube of a number is denoted , using a superscript 3, for example . The cube Mathematical ...
– (3
superscript A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, wh ...
) * Thrice * Third * Triad * Trio * Rule of three * ɜ, also known as Reversed epsilon


References

*Wells, D. ''
The Penguin Dictionary of Curious and Interesting Numbers ''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, a ...
'' London: Penguin Group. (1987): 46–48


External links


Tricyclopedic Book of Threes
by Michael Eck

by John A. McNulty *
The Number 3The Positive Integer 3
{{DEFAULTSORT:3 (Number) Integers